Would anyone know when is the last date this year that I will be able to take the RHEL 7 RHCSA 124 exam?
You have a bit of a mix here. "124" is the ID of the "Red Hat System Administration 1" course (full code RH124), not the EXAM.
The RHCSA for RHEL7 recommends both courses;
1. RH124 (Red Hat System Administration 1) and
2. RH134 (Red Hat System Administration 2)
The exam for RHCSA certification is actually called EX200. And the exam will be available until May 7, 2020. You can read about this in the EX200 page here:
Notice that this page was updated for the RHEL8 version of the EX200, but there is a blue box, right below the description, with the text and a link to RHEL7 information:
"The exam based on Red Hat Enterprise Linux 7 is available via on-site and individual exams. Details"
Hope this helps!